For a certain river, suppose the drought length Y is the number of consecutive time intervals in which the water supply remains below a critical value y0 (a deficit), preceded by and followed by periods in which the supply exceeds this critical value (a surplus). An article proposes a geometric distribution with p = 0.389 for this random variable.
(a) What is the probability that a drought lasts exactly 3 intervals?
(b) At most 3 intervals?
(c) What is the probability that the length of a drought exceeds its mean value by at least one standard deviation?

Question

For a certain river, suppose the drought length Y is the number of consecutive time intervals in which the water supply remains below a critical value y0 (a deficit), preceded by and followed by periods in which the supply exceeds this critical value (a surplus). An article proposes a geometric distribution with p = 0.389 for this random variable.
(a) What is the probability that a drought lasts exactly 3 intervals? 
(b) At most 3 intervals?
(c) What is the probability that the length of a drought exceeds its mean value by at least one standard deviation?